### Find the equation of the regression line

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Assignment

Question 1

Use this extract taken from the article, "Goji berries prevent macular degeneration," (appeared in Healthy Foods, Healthy Bodies on January 21, 2016) to answer the questions that follow:

Goji berries (Lycium barbarum L.) are thought to benefit vision because of their high antioxidant content. The macular, an important pigmented area near the center of the retina of the eye, is responsible for central vision. In the elderly, macular-degeneration is a primary cause of failing eye-sight. A recent study by scientists at the Nestlé Research Centre, Switzerland and Shanghai Jiao Tong University School of Medicine investigated the effects of daily supplementation of a mixture of goji berries and lacto-wolfberry on macular characteristics of the eyes in elderly subjects.

A double-blind, randomised, placebo-controlled trial was conducted with 150 healthy elderly subjects aged 65 to 70 years. Randomisation was stratified by gender. For a period of 90 days, 75 randomly selected participants were assigned to receive the mixture of berries in a powdered form mixed in with their daily lunch-time soup, while the remaining 75 participants were given a powdered mixture that did not contain the active ingredients with their usual soup. Before and after the 90 days of the trial, the elderly subjects underwent eye examinations to assess pigmentation and the presence of age-related macular degeneration.

It was found that the daily dietary supplementation with goji berry and lacto- wolfberry for 90 days increases antioxidant levels as well as protects from hypopigmentation in the macula of elderly subjects, reducing the risk of macular- degeneration. However, the mechanism of action is unclear.

(a) Is this particular study that was cited in the article observational or experimental? In less than 50 words clearly explain your choice based on the extract given above.

(b) Identify the variable(s) of interest.

(c) Explain what is meant by ‘double-blind, randomised, placebo controlled trial' in the context of the study.

(d) Explain what is meant by ‘Randomisation was stratified by gender'. Why might the researchers in this study decide to ‘stratify by gender'?

Question 2

High total cholesterol was the second greatest attributor to the total burden of heart disease in Australia, according to the Heart Foundation. Of great concern is the number of younger people with a high total cholesterol level. In fact, 25% of adults aged 25-34 years have a higher than normal total cholesterol level.

A random sample of 12 people between the ages of 25 and 34 years were selected from the Springfield campus to have their total cholesterol level checked. The variable of interest is the number of people between the ages of 25 and 34 years who have a high total cholesterol level.

Use this information to answer the following questions:

(a) Suggest an appropriate model to estimate the probabilities of the number of people between the ages of 25 and 34 years who have a high total cholesterol level.

i. What are the parameters of this model for this context?
ii. Explain why this model is appropriate by discussing the important distinguishing features of the model.

(b) Using the model from part (a), estimate the probability that, in the randomly selected sample of 12 people from Springfield campus aged 25 to 34 years, 3 or less will have a high total cholesterol level.

(c) A random sample of 120 people aged between 25 and 34 years have been selected from the Toowoomba campus to have their cholesterol level checked. For this sample of 120, estimate the mean and standard deviation of the number of people aged 25 to 34 years who have a high total cholesterol level.

(d) Determine the probability that, in the random sample of 120 people (selected in part (c)), 20 or more will have a high total cholesterol level.

(e) State and check any assumptions, conditions or rules of thumb that should be considered before performing the calculations to determine the probability in part (d).

Question 3

This question uses information from the data file diabetes16.sav found under the Assignments and Datasets link on the StudyDesk (also see diabetes.txt for more details about the health study and the variables measured). Make sure the variable view in SPSS is setup correctly with all ‘labels' correctly defined (with units), all ‘values' assigned correctly for categorical variables and the correct ‘measure' selected for all variables.

As a researcher seeking to gain insights into the variables measured in this study, you are interested in ascertaining if there is a relationship between gender and body frame (build) of African American people living in Virginia.

(a) Using SPSS, produce a contingency table to display the relationship between Gender and Body Frame for participants in this study. The title for this table should reflect the table contents and also include your name. (Note that a table title should appear above the table). You can copy and paste this table straight into your assignment; just ensure you have a meaningful title.

(b) With reference to this study, what proportion of males have a large body frame?

(c) With reference to this study, what proportion of people with a small body frame are female?

(d) Based on the data from this study, does there appear to be an association between Gender and Body Frame in the population of African Americans living in Virginia? Explain in less than 100 words, using a numerical example(s) from a conditional distribution table to support your explanation.

Question 4

The time to microwave a 50 gram bag of Crunchy Corn popcorn using an automatic setting on an 800W microwave oven has an approximate normal distribution with a mean of 200 seconds and a standard deviation of 18 seconds.

(a) Identify the variable of interest and the unit of measurement of the variable.

(b) The manufacturers of Crunchy Corn want to be as accurate as possible with their labelling. What time should they quote on their packaging such that no more than 5% of their 50 gram bags will take longer than this time to pop, under the stated conditions?

(c) What proportion of 50 gram bags of Crunchy Corn popcorn will take less than 3 minutes to pop under these conditions?

(d) What proportion of 50 gram bags of Crunchy Corn popcorn will take between 2 and a half and 3 and a half minutes to pop under these conditions?

Question 5

Consider the data in the file diabetes16.sav again. Use SPSS to find the answers to the following questions, but do not copy and paste SPSS output into your answer for parts (c) and (d) (make sure you always include units where appropriate).

(a) Display the distribution of Total Cholesterol Level of the African Americans in this study, using an appropriate graph. Label the axes correctly, include units of measure and provide an appropriate title. Include your name in the title of your graph.

(b) Using the graph in (a) only (don't refer to SPSS summary statistics), describe in no more than 60 words, the distribution of Total Cholesterol Level. Include comments on shape, centre and spread of the distribution and the existence of outliers, if any. Do not include information from any calculations, use the graph only.

(c) What is the sample size, mean and standard deviation of the distribution of Total Cholesterol Level of participants in the study? (Use SPSS, but do not just copy/paste SPSS output).

(d) Using SPSS find the median and IQR of the distribution of Total Cholesterol Level of participants in the study? (Do not copy/paste SPSS output).

(e) For the distribution of Total Cholesterol Level in part (a), which statistics are appropriate to measure the centre and spread? Give a reasonable explanation for your choice.

Question 6

Consider the data in the file diabetes16.sav again. As a researcher you are interested in seeing if Stabilised Glucose Level can be used effectively to predict Glycosylated Haemoglobin Percentage, especially since the test for Stabilised Glucose Level is more cost effective in monitoring the impact of diabetes on cardiovascular disease.

(a) What are the two variables you will need to include in your analysis? What type of variables are they? What are the units of these variables?

(b) Use an appropriate graph to display the relationship between the two variables identified in part (a) for the participants in this study. Label the axes correctly, include units of measure and provide an appropriate title. Include your name in the title of your graph.

(c) From the graph in part (b), describe (in no more than 30 words) the form, direction and scatter of this relationship, and identify any outliers.

(d) Calculate an appropriate statistic to measure the strength and direction of the relationship between the two variables for these participants. Interpret this statistic.

(e) Use SPSS to find the equation of the regression line which could be used to predict an individual's glycosylated haemoglobin percentage from their stabilised glucose level:

i. State the regression equation,
ii. Plot the regression line on the graph in part (b),
iii. Interpret the slope of the regression line,
iv. Interpret the intercept of the regression line.

(f) Do you think this procedure is a ‘good' method for predicting an individual's glycosylated haemoglobin percentage from their stabilised glucose level? Give two reasons to support your decision.

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#### len1457949

4/11/2017 1:24:22 AM

#### len1457949

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• Answering the questions in this assignment should not be your first attempt at these types of questions. It is essential that you work through practice exercises from the tutorial sheets and/or text book first. • This assignment is important in providing feedback and helping to establish competency in essential skills. • Answer all the questions. The questions are not of equal weight; some questions are worth much more than others. • The questions relate to material in Modules 1 to 6. • Before starting this assignment read Notes Concerning Assignments under the Introductory Material link on the StudyDesk.

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